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Journal of Arid Land  2022, Vol. 14 Issue (12): 1344-1360    DOI: 10.1007/s40333-022-0109-6
Research article     
Runoff characteristics and its sensitivity to climate factors in the Weihe River Basin from 2006 to 2018
WU Changxue1, Xu Ruirui2,3, QIU Dexun2,3, DING Yingying1, GAO Peng1,2,3,*(), MU Xingmin1,2,3,*(), ZHAO Guangju1,2,3
1State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Northwest A&F University, Yangling 712100, China
2State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau, Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling 712100, China
3University of Chinese Academy of Sciences, Beijing 100000, China
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Exploring the current runoff characteristics after the large-scale implementation of the Grain for Green (GFG) project and investigating its sensitivities to potential drivers are crucial for water resource prediction and management. Based on the measured runoff data of 62 hydrological stations in the Weihe River Basin (WRB) from 2006 to 2018, we analyzed the temporal and spatial runoff characteristics in this study. Correlation analysis was used to investigate the relationships between different runoff indicators and climate-related factors. Additionally, an improved Budyko framework was applied to assess the sensitivities of annual runoff to precipitation, potential evaporation, and other factors. The results showed that the daily runoff flow duration curves (FDCs) of all selected hydrological stations fall in three narrow ranges, with the corresponding mean annual runoff spanning approximately 1.50 orders of magnitude, indicating that the runoff of different hydrological stations in the WRB varied greatly. The trend analysis of runoff under different exceedance frequencies showed that the runoff from the south bank of the Weihe River was more affluent and stable than that from the north bank. The runoff was unevenly distributed throughout the year, mainly in the flood season, accounting for more than 50.00% of the annual runoff. However, the trend of annual runoff change was not obvious in most areas. Correlation analysis showed that rare-frequency runoff events were more susceptible to climate factors. In this study, daily runoff under 10%-20% exceeding frequencies, consecutive maximum daily runoff, and low-runoff variability rate had strong correlations with precipitation, aridity index, and average runoff depth on rainy days. In comparison, daily runoff under 50%-99% exceeding frequencies, consecutive minimum daily runoff, and high-runoff variability rate had weak correlations with all selected impact factors. The sensitivity analysis results suggested that the sensitivity of annual runoff to precipitation was always higher than that to potential evaporation. The runoff about 87.10% of the selected hydrological stations were most sensitive to precipitation changes, and 12.90% were most sensitive to other factors. The spatial pattern of the sensitivity analysis indicated that in relatively humid southern areas, runoff was more sensitive to potential evaporation and other factors, and less sensitive to precipitation.

Key wordsdaily runoff      climate-related factors      precipitation      potential evaporation      correlation analysis      sensitivity analysis      Weihe River Basin     
Received: 19 July 2022      Published: 31 December 2022
Corresponding Authors: *GAO Peng (E-mail:;MU Xingmin (E-mail:
Cite this article:

WU Changxue, Xu Ruirui, QIU Dexun, DING Yingying, GAO Peng, MU Xingmin, ZHAO Guangju. Runoff characteristics and its sensitivity to climate factors in the Weihe River Basin from 2006 to 2018. Journal of Arid Land, 2022, 14(12): 1344-1360.

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Fig. 1 Topography, river networks, and hydrological stations of the Weihe River Basin (WRB)
Index Unit Description and calculation
Q1, Q5, Q10, Q20, Q50, Q80, Q90, Q95, and Q99 mm/d Daily runoff under different exceeding frequencies. The subscript represents the percentage of runoff exceedance probability.
Min1, Min7, and Min30 mm Consecutive minimum daily runoff. The subscript indicates the consecutive days.
Max1, Max7, and Max30 mm Consecutive maximum daily runoff. The subscript indicates the consecutive days.
RQ95:Q50 and RQ5:Q50 / Low-runoff variability rate and high-runoff variability rate, respectively. Annual runoff is divided by the median annual runoff, providing an overview of how the flow duration curve changes over time.
RC / Ratio of annual runoff to precipitation, reflecting the average water production capacity of the basin during a certain period.
R mm Annual runoff.
Table 1 Description and calculation of runoff characteristic indices
Predictor Unit Calculation
Annual precipitation (P) mm $\text{P}=\sum\limits_{\text{i}=1}^{12}{{{\text{P}}_{i}}}$,
where i refers to the month; and Pi is the monthly precipitation (mm).
Precipitation seasonality (Psi) / Psi is calculated as follows (Walsh and Lawler, 1981):
${{\text{P}}_{\text{si}}}={{\text{P}}^{-1}}\sum{\left| {{\text{P}}_{i}}-\text{P}/12 \right|}$.
Average rain depth (α) mm/d Mean precipitation during rainy days.
Annual potential evaporation (Ep) mm Ep is calculated by a modified version of the Hargreaves (Droogers and Allen, 2002):
${{E}_{p}}=0.0013\times 0.408\times RA\times ({{\text{T}}_{av}}+17)\times {{(\text{TD}-0.0123\text{P})}^{0.76}}$,
where Tav is the average of the mean maximum temperature and minimum temperature for each month (°C); TD represents the difference between the average maximum temperature and minimum temperature per month (°C); and RA represents the extraterrestrial radiation (MJ/(m2•d)), which were acquired from Food and Agriculture Organization (FAO) of the United Nations.
Potential evaporation seasonality (Ep si) / Ep si is calculated as follows (Walsh and Lawler, 1981):
${{\text{E}}_{\text{p }}}_{\text{si}}={{\text{E}}_{\text{p}}}^{-1}\sum{\left| {{\text{E}}_{\text{p}}}_{\text{m}}-{{\text{E}}_{\text{p}}}/12 \right|}$,
where Ep and Epm are the annual and monthly potential evaporation (mm), respectively.
Aridity index (ϕ) / $\phi \text{=}\frac{{{\text{E}}_{\text{p}}}}{\text{P}}$.
Seasonal correlation between water supply and demand (CORR) / CORR is the correlation coefficient between monthly precipitation and annual potential evaporation (Petersen et al., 2012).
Average annual temperature (TA) K $\text{TA}=\sum\limits_{\text{i}=1}^{12}{\left( {{\text{T}}_{i}}+274.15 \right)}/12$,
where Ti is the monthly mean air temperature of the ith month (°C).
Table 2 Climate-related characteristics selected to estimate the runoff characteristics
Fig. 2 (a), flow duration curves (FDCs) of daily runoff in the WRB with three distinct ranges of mean annual runoff (MAR); (b), spatial distribution of hydrological stations with different ranges of MAR. Red, green, and blue sites are 6, 45, and 11 of the 62 stations, respectively, where MAR varied from 3.43 to 13.33 mm, from 20.92 to 109.30 mm, and from 229.03 to 507.25 mm, respectively.
Fig. 3 Spatial distributions of runoff trends under high-frequency runoff events (Q95; a), intermediate-frequency runoff events (Q50; b), and rare-frequency runoff events (Q5; c)
Station Hydrological element Jan (mm) Feb (mm) Mar (mm) Apr (mm) May (mm) Jun (mm) Jul (mm) Aug (mm) Sep (mm) Oct (mm) Nov (mm) Dec (mm) Proportion in flood season (%)
Linjiacun Precipitation 6.75 12.36 28.45 42.01 67.83 79.81 125.67 117.11 129.45 51.22 19.95 3.34 66.09
Runoff 1.14 0.82 1.18 1.68 2.26 2.11 5.86 4.14 4.47 3.48 1.70 1.34 54.94
Xianyang Precipitation 6.38 9.91 23.41 36.78 60.26 54.16 103.21 100.87 105.06 47.98 20.56 3.67 63.49
Runoff 2.03 1.77 2.07 3.21 3.97 4.05 8.22 7.25 11.29 7.64 4.26 2.69 52.71
Huaxian Precipitation 4.36 8.85 17.37 36.79 59.82 50.17 90.58 79.21 98.98 43.32 26.11 4.48 61.33
Runoff 1.86 1.53 1.84 2.95 3.54 2.78 6.36 6.04 8.95 6.01 3.62 2.26 50.54
Zhangjiashan Precipitation 6.48 9.48 23.07 34.05 47.83 56.15 88.88 75.76 95.82 38.58 18.12 3.34 63.63
Runoff 0.97 1.11 1.60 1.28 1.18 1.21 4.05 3.83 3.33 2.29 1.68 1.23 52.27
Zhuangtou Precipitation 4.20 8.80 13.24 29.63 50.93 54.05 87.05 77.34 82.67 42.42 20.36 2.19 63.68
Runoff 0.82 0.99 1.68 1.39 1.16 1.06 3.19 2.99 3.12 2.18 1.51 1.16 48.75
Total Precipitation 5.64 9.88 21.11 35.85 57.34 58.87 99.08 90.06 102.40 44.70 21.02 3.40 63.79
Runoff 0.99 0.94 1.29 1.53 1.69 1.52 3.85 3.50 4.41 3.03 1.87 1.26 51.31
Table 3 Distribution of monthly precipitation and runoff in the Weihe River basin (WRB)
Fig. 4 Spatial distributions of annual runoff trends in different subintervals
Index P Psi α Ep Ep si ϕ CORR TA
Q1 0.72+lin 0.22+pow 0.64+pow 0.20-pow 0.06-pow 0.69-pow 0.46+exp 0.29-pow
Q5 0.72+pow 0.16+pow 0.70+lin 0.17-pow 0.14-log 0.64-pow 0.34+log 0.17-exp
Q10 0.78+pow 0.14+pow 0.63+pow 0.16-exp / 0.69-pow 0.34+log 0.22-exp
Q20 0.68+exp 0.06+pow 0.32+pow 0.25-exp 0.05+lin 0.49-pow 0.20+log 0.42-exp
Q50 0.06+pow 0.22+lin / 0.30-exp / 0.12-exp 0.06+lin 0.43-exp
Q80 / 0.18+lin 0.08-lin 0.06-lin / / 0.05+lin 0.21-log
Q90 / 0.15+lin / / / / 0.15+lin 0.12-lin
Q95 / 0.07+lin / / 0.06-lin / 0.15+lin 0.09+lin
Q99 / / / 0.07+exp 0.07-lin / 0.19+lin /
Max1 0.58+exp 0.35+pow 0.48+exp 0.23-pow / 0.59-pow 0.50+lin 0.37-exp
Max7 0.81+exp 0.18+pow 0.66+pow 0.15-pow / 0.75-pow 0.38+lin 0.23-exp
Max30 0.75+pow 0.18+pow 0.62+pow 0.17-pow / 0.72-pow 0.42+lin 0.26-exp
Min1 / / / / 0.15-lin / 0.22+lin /
Min7 / / 0.04+pow 0.08+exp 0.07-lin / 0.11+lin /
Min30 0.07-lin / 0.13-lin / / / 0.05+lin 0.05-lin
RQ95:Q50 0.08+pow / 0.12+pow 0.06-pow / 0.19+exp / 0.12+pow
RQ5:Q50 0.71+pow 0.09+lin 0.75+pow 0.07-pow 0.12-log 0.57-pow 0.28+pow 0.05-exp
RC 0.40+lin 0.17+exp 0.22+pow 0.25-pow / 0.27-pow 0.26+lin 0.56-exp
MAR 0.69+pow 0.13+exp 0.45+pow 0.23-pow / 0.62-pow 0.35+lin 0.36-exp
Table 4 R2 values between runoff characteristics and climate-related factors
Fig. 5 Distribution of spatial hydrological and climatic characteristics in the study area based on the Budyko framework. (a-c), spatial pattern of the runoff ratio, aridity index, and other factors, respectively; (d-f), values of the runoff ratio, aridity index, and other factors at different hydrological stations, respectively.
Fig. 6 Absolute sensitivities of runoff to precipitation (εR,P; a), annual potential evaporation (εR,Ep; b), and other factors (εR,ω; c) in the WRB. (d-f), values of εR,P, εR,Ep, and εR,ω at different hydrological stations, respectively.
Fig. 7 Relative sensitivities of runoff to precipitation (θP), potential evaporation (θEp), and other factors (θω) at different hydrological stations
Fig. 8 FDCs for daily precipitation of 62 meteorological stations in the WRB
Fig. 9 Spatial distribution of mean annual precipitation (MAP; a), mean precipitation in rainy days (α; b), the ratio of wet to dry days (f; c), the seasonal correlation between water supply and demand (CORR; d), mean annual potential evaporation (Ep; e), and average annual temperature (TA; f) in the WRB
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